Virgil
Posts:
4,661
Registered:
1/6/11
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Re: Matheology 203
Posted:
Feb 7, 2013 3:27 AM
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In article
<30e6f8dd-f487-4335-ba77-35f182b79b05@e10g2000vbv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 7 Feb., 08:53, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <457d0429-33c1-46ad-9151-4f5d9dc96...@fv9g2000vbb.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 7 Feb., 05:21, fom <fomJ...@nyms.net> wrote:
> >
> > > > Or as Virgil would write
> >
> > > in a very lucid moment:
> >
> > > > What Cantor proved was that no list of accessible real numbers
> > > > (accessible because listable) can include all accessible numbers,
> > > > because any such list itself proves the existence of numbers not listed.
> >
> > > That is, Cantor proved the countable set of accessible numbers being
> > > uncoutable.
> >
> > That may well be WM's misunderstanding but it is not an understanding.
> >
> > A number being accessible does means that it can appear in some list,
> > but does not at all mean that all accessible numbers can appear together
> > in a single list.
>
> All elements of countable sets can be counted by definition, i.e.,
> they can appear in a list.
But some subsets of a set may be countable even though the set itself is
not. Certainly SOME sets of reals can be counted but not every set of
reals can be counted.
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